Electronic Research Announcements Of The AMS surgery. Hutchings, Michael Michael Hutchings; Frank Morgan; ManuelRitor? Antonio Ros Proof of the double bubble conjecture. Kamber http://www.kurims.kyoto-u.ac.jp/EMIS/journals/ERA-AMS/era-auth-2000.html
Computer Images Of Double Bubbles By John Sullivan I created these images to illustrate the proof of the equalvolume caseof the double bubble conjecture by Hass and Schlafly in 1995. http://torus.math.uiuc.edu/jms/Images/double/
Extractions: These images show bubble clusters near equilibrium. The top row shows a standard double bubble of equal volumes, and a nonstandard cluster in which one bubble is a torus, forming a waist around the other. I created these images to illustrate the proof of the equal-volume case of the Double Bubble Conjecture by Hass and Schlafly in 1995. The bottom row shows a standard double bubble of unequal volumes (consisting of three spherical caps meeting at equal 120-degree angles), and a nonstandard bubble of the same volumes, in which the larger region is broken into two components (one a tiny ring around the other region). I created these images to illustrate the proof of the general Double Bubble Conjecture by Hutchings, Morgan, Ritore and Ros in 2000. In all four cases, the cluster is a surface of revolution. More details about the geometry of the examples with unequal volumes, including pictures of the generating curves, are available
Historia Matematica Mailing List Archive: [HM] Double Bubble Co HM double bubble conjecture Proved. Proof of the double bubble conjecture. by MichaelHutchings, Frank Morgan, Manuel Ritore, and Antonio Ros. quote History. http://sunsite.utk.edu/math_archives/.http/hypermail/historia/mar00/0093.html
Historia Matematica Mailing List Archive: Re: [HM] Copernicus' Pythagoras, Ptolemy and Hilbert ; Previous message Antreas P. Hatzipolakis HM double bubble conjecture Proved ; In reply to Antreas http://sunsite.utk.edu/math_archives/.http/hypermail/historia/mar00/0094.html
Lecture 4 Frank Morgan will give nine lectures on the subject of Geometric MeasureTheory and the Proof of the double bubble conjecture. Last http://zeta.msri.org/calendar/talks/TalkInfo/504/show_talk
Extractions: Last year Hutchings, Morgan, Ritore and Ros announced a proof of the Double Bubble Conjecture, which says that the familiar standard double soap bubble provides the least-area way to enclose and separate two given volumes of air. It was only with the advent of geometric measure theory in the 1960s that mathematicians were ready to deal with such problems involving surfaces meeting along singularities in unpredictable ways. The lectures will discuss modern, measure-theoretic definitions of "surface," compactness of spaces of surfaces, and finally the proof of the double bubble conjecture. Homework will vary from basic exercises to open problems. The text Geometric Measure Theory: A Beginner's Guide (3rd edition) by Frank Morgan will be made available, as well as additional notes and materials. (Students nominated by MSRI sponsors will receive a copy of the book on arrival. Several copies will be available for use by other participants.) There will be sessions on exercises and on open problems.
Electronic Research Announcements Of The AMS Hutchings, Michael Michael Hutchings; Frank Morgan; Manuel Ritoré; Antonio Ros Proofof the double bubble conjecture. Kirillov, AA AA Kirillov Family algebras. http://www-sbras.nsc.ru/EMIS/journals/ERA-AMS/era-auth-2000.html
Electronic Research Announcements Of The AMS quasiconformal surgery. 53A10 Michael Hutchings; Frank Morgan; Manuel Ritoré;Antonio Ros Proof of the double bubble conjecture. 53C42 Michael http://www-sbras.nsc.ru/EMIS/journals/ERA-AMS/era-msc-2000.html
Mathenomicon.net : News : Double Bubbles A proof of the double bubble conjecture has been announced at theRoseHulman Institute of Technology in Indiana, United States. http://www.cenius.net/news/news.php?ArticleID=0
Mathenomicon.net : News : Archive 21th March 2000 Double bubbles A proof of the double bubble conjecture has been announcedat the RoseHulman Institute of Technology in Indiana, United States. http://www.cenius.net/news/archive/default.php
Department Of Mathematics - Clanton Visiting Mathematician PROOF OF THE double bubble conjecture ABSTRACT A single round soap bubble providesthe most efficient, leastarea way to enclose a given volume of air. http://math.furman.edu/activities/clanton/
Extractions: ABSTRACT: A single round soap bubble provides the most efficient, least-area way to enclose a given volume of air. The Double Bubble Conjecture says that the familiar double soap bubble which forms when two soap bubbles come together provides the most efficient way to enclose and separate two given volumes of air. We'll discuss the problem, the recent proof, important contributions by undergraduates, and remaining open problems.
Department Of Mathematics - Colloquium Abstracts Proof Of the double bubble conjecture. Frank Morgan Williams College 26September 2002. ABSTRACT TBA Raymond Pearl and the Logistic Curve. http://math.furman.edu/activities/colloquium/abstracts/
Extractions: 10 October 2002 ABSTRACT : We will discuss some of the early history of the population ecology, then look at the development of the logistic model, beginning with Pierre-Francois Verhulst. We will conclude with an in-depth look at the campaign by Raymond Pearl to establish the logistic model as a "law" of population growth. Origins of Abstraction in Algebra, 24 October 2002 ABSTRACT :Algebra is essentially the study of systems of polynomial equations, although current treatments of the subject can thoroughly disguise this fact. We will consider how certain classical problems involving polynomials, such as Fermat's last theorem and the insolubility of the quintic, eventually led to the more general and abstract approach that algebraists take today. This fundamental change in perspective was in large part due to the work of Emmy Noether, who not only clarified and consolidated recent results, but more importantly demonstrated the utility of this viewpoint in breaking new ground. The Method of Archimedes John Poole 7 November 2002 ABSTRACT : When Archimedes came into the mathematical world, mathematicians knew how to find the volumes of cylinders and cones, but not spheres. We will see how Archimedes used "The Law of the Lever" to obtain a relationship between a sphere, a cylinder, and a cone, and thus how to find the volume of a sphere. Although Archimedes used only simple geometric facts, we can see how his manipulations brought him close to discovering integral calculus.
Double Bubble 159, 4759, 1993. Morgan, F. ``The double bubble conjecture.'' FOCUS 15,6-7, 1995. Peterson, I. ``Toil and Trouble over Double Bubbles.'' Sci. http://www.ph.tn.tudelft.nl/Internal/PHServices/Documentation/MathWorld/math/mat
Extractions: References Campbell, P. J. (Ed.). Reviews. Math. Mag. Foisy, J.; Alfaro, M.; Brock, J.; Hodges, N.; and Zimba, J. ``The Standard Double Soap Bubble in Uniquely Minimizes Perimeter.'' Pacific J. Math. Morgan, F. ``The Double Bubble Conjecture.'' FOCUS Peterson, I. ``Toil and Trouble over Double Bubbles.'' Sci. News , 101, Aug. 12, 1995.
Double Bubble Minimizes: Applications To Geometry J. Hass, M. Hutchings, and R. Schlafly, The double bubble conjecture, ElectronicResearch Announcements of the American Mathe. Society, 1995, Vol. 1, pp. http://www.lsi.upc.es/~robert/mirror/interval-comp/bubble.html
Extractions: It is well known that of all surfaces surrounding an area with a given volume V, the sphere has the smallest area. This result explains, e.g., why a soap bubble tends to become a sphere. More than a hundred years ago, the Belgian physicist J. Plateaux asked a similar question: what is the least area surface enclosing two equal volumes? Physical experiments with bubbles seem to indicate that the desired least area surface is a "double bubble", a surface formed by two spheres (separated by a flat disk) that meet along a circle at an angle of 120 degrees. However, until 1995, it was not clear whether this is really the desired least area surface. Several other surfaces ("torus bubbles") have been proposed whose areas are pretty close to the area of the double bubble. The theorem that double bubble really minimizes was recently proven by Joel Hass from Department of Mathematics, University of California at Davis (email hass@math.ucdavis.edu
Extractions: Program for weeks one and two The first two weeks of the 2001 Clay Mathematics Institute will include a graduate level introduction to the theory of minimal surfaces. There will be two or three lecture series and additional events and activities, including homework sessions, open problem discussions, demonstrations and instruction on computer graphics techniques. Attending will be graduate students from the MSRI sponsoring institutions and additional graduate students and researchers sponsored by the Clay Institute. Attending students are nominated by an MSRI sponsor or nominated as a Clay Mathematics Institute participant via the methods indicated in the CMI Workshop Page at the Clay Research Institute on The Global Theory of Minimal Surfaces. For the main program see the MSRI Workshop Page for the Clay Research Institute on The Global Theory of Minimal Surfaces Main Lecture Series - Topics Frank Morgan will give nine lectures on the subject of Geometric Measure Theory and the Proof of the Double Bubble Conjecture: Last year Hutchings, Morgan, Ritore and Ros announced a proof of the Double Bubble Conjecture, which says that the familiar standard double soap bubble provides the least-area way to enclose and separate two given volumes of air. It was only with the advent of geometric measure theory in the 1960s that mathematicians were ready to deal with such problems involving surfaces meeting along singularities in unpredictable ways. The lectures will discuss modern, measure-theoretic definitions of "surface," compactness of spaces of surfaces, and finally the proof of the double bubble conjecture. Homework will vary from basic exercises to open problems. The text
Streaming Video - Spring 2001 June 25 July 6, 2001. Lecture Series Frank Morgan Geometric MeasureTheory and the Proof of the double bubble conjecture, Lecture 1; http://www.msri.org/publications/video/index02.html
BBC News | SCI/TECH | Double Bubble Is No Trouble Four mathematicians have announced a proof of the socalled double bubble conjecture- that the familiar double soap bubble is the optimal shape for enclosing http://news.bbc.co.uk/hi/english/sci/tech/newsid_685000/685243.stm
Extractions: By BBC News Online science editor Dr David Whitehouse Four mathematicians have announced a proof of the so-called Double Bubble Conjecture - that the familiar double soap bubble is the optimal shape for enclosing and separating two chambers of air. In an address to the Undergraduate Mathematics Conference at the Rose-Hulman Institute of Technology in Indiana, Frank Morgan of Williams College, Massachusetts, announced that he, Michael Hutchings of Stanford, and Manuel Ritori and Antonio Ros of Granada, had finally proved what the double soap bubble had known all along. When two round soap bubbles come together, they form a double bubble. Unless the two bubbles are the same size, the surface between them bows a bit into the larger bubble. The separating surface meets each of the two bubbles at 120 degrees. Mathematicians have expressed surprise that when two bubbles are joined in this way that the interior surface that separates them is not bowed all that much.
Student Papers At The NES/MAA Spring 2000 Meeting Session I double bubble conjectures Andrew Cotton, Harvard University and WilliamsCollege The double bubble conjecture in R 3 has recently been proved. http://www.southernct.edu/organizations/nesmaa/studentpapersspring2000.html
Cwikel Frank Morgan Williams College Proof of the double bubble conjecture.Abstract. The double bubble conjecture says that the familiar http://www.math.princeton.edu/~seminar/2002-03-sem/MorganAbstract10-7-2002.html
Seminar Week of October 7 October 11, 2002. Analysis Seminar. Topic Proof ofthe double bubble conjecture. Presenter Frank Morgan, Williams College. http://www.math.princeton.edu/~seminar/2002-03-sem/9-26-2002weekly.html
Extractions: PACM Colloquium Topic: The Level Set Method and Schroedinger's Equation Presenter: Li-Tien Cheng , University of California, San Diego Date: Monday, September 30, 2002, Time: 4:00 p.m., Location: Fine Hall 214 Abstract: The level set method has recently been succesfully applied to the construction wavefronts in geometrical optics. We extend the approach here to wavefronts found in Schroedinger's equation as well as other quantities of interest. Advantages such as an Eulerian foundation and the ability to handle multivaluedness are preserved in the extension.
ScienceDaily: Computers & Math News Summaries 0320 Mathematicians Prove Double Soap Bubble Had It Right Four mathematicians haveannounced a mathematical proof of the double bubble conjecture that the http://www.sciencedaily.com/news/computers_summaries.php?page=370
